For manufacturing next-generation high-precision optical elements required for lithography techniques using X-ray free electron laser and extreme-ultra violet rays with a wavelength of 13.5 nm, it is essential to measure the shapes of aspheric and free-form surfaces with precisions of 1 to 0.1 nm RMS. Such X-ray optical elements, typically X-ray reflection mirrors, need to have a size of 10 to 500 cm and attain the foregoing precisions over the entire reflection surfaces. In addition, there is also demand for ultra-precision shape measurement of mass-produced consumer-use aspheric mirrors and lenses with various curvatures. As means for measuring surface roughness with a space wavelength of 1 mm or less, probe microscopes with atomic-level resolutions meet precision requirements under the present situation. However, the probe microscopes are capable of measurement at one time in an extremely small range of about 50 μm in all directions, and take long measurement time and thus are not suited for measuring the shape of an entire object to be measured. Meanwhile, as a technique for shape measurement with a space wavelength of 1 mm or more, Long Trace Profilers (LTPs) are used to irradiate an object to be measured with a narrow laser beam with a diameter of about 1 mm and measure obtained displacements of reflected light to determine inclination angles on the surface of the object. The measurement technique achieves a measurement precision of 5×10−7 rad RMS (3 nm RMS), but is only for two-dimensional shape measurement with a limited measurement range off ±5 m rad. In addition, point light source interferometry achieves a measurement precision of 0.3 nm RMS, but in principle in this measurement method, spherical waves from a point light source are referred to, which makes it difficult to measure the shapes of aspheric surfaces.
To solve the foregoing conventional issue, Patent Literatures 1 and 2 each suggest an ultra-precision shape measurement method. In the principle of the shape measurement method, the straight-ahead moving property of light is utilized to trace a normal vector on the surface of an object; two pairs of biaxial goniometers are subjected to follow-up control with feedback of QPD output, so as to allow a laser beam emitted from a light source to be reflected by a mirror and returned to the center of a detector (quartered photodiode: QPD) positioned at the light source; and a uniaxial straight-ahead stage along the direction of an optical axis is subjected to follow-up control with feedback of QPD output, so as to keep constant a light path length (L) between the detector and the surface of the object to be measured, thereby realizing a null method with alignment of incoming and reflecting lights and higher-speed measurement. Specifically, one pair of goniometers constitutes a sample system and holds the object to be measured at its movable part, and the other pair of goniometers constitutes an optical system and has the light source and the QPD at its movable part, and the sample system or the optical system is driven by the uniaxial straight-ahead stage. Normal vectors at arbitrary measurement points (coordinates) on the mirror are determined by outputs from encoders of the goniometers, and the shape of the object is derived from the measurement data.
According to the normal vector tracing ultra-precision shape measurement method disclosed in Patent Document 1, on measurement of coordinates and normal vectors at measurement points, one pair of biaxial goniometers is instructed to measure the measurement point coordinates, output from the QPD is read into a computer, the other pair of biaxial goniometers is controlled to make the output minimum, and then outputs from a five-axis linear encoder on the straight-ahead stage keeping constant the light path length L, which is controlled separately from four-axis rotary encoders, are read simultaneously. Conventionally, the two pairs of biaxial goniometers and the uniaxial straight-ahead stage along the direction of an optical axis are subjected to semi-closed feedback control to achieve shape measurement with a shape precision of 2 nm RMS and a slope error of 5×10−7 rad RMS. However, the measurement method uses semi-closed feedback control using computers, and thus takes several hours of measurement time and is susceptible to influence of disturbance factors such as temperature changes or the like.
Accordingly, Patent Literature 2 discloses an invention of a measurement method in which, of two pairs of biaxial goniometers and a uniaxial straight-ahead stage, the biaxial goniometers constituting an optical system and the uniaxial straight-ahead stage are subjected to fully-closed feedback control under which output from a light detector is input directly into an axis drive motor, and the biaxial goniometers constituting a sample system are subjected to semi-closed feedback control, thereby allowing quick measurement of normal vectors at measurement point coordinates and short-time measurement of the surface shapes of objects. In addition, the method disclosed in Patent Literature 2 allows precision measurement of the shapes of large-sized objects.